1. Field of the Invention
This invention relates to a method of designing a natural laminar flow wing of an actual supersonic aircraft, and in particular relates to a method of designing a natural laminar flow wing which, in addition to reduction of pressure drag, which has been a goal in the past in design of a supersonic aircraft, reduces friction drag by delaying the boundary layer transition at the wing surface in flight conditions similar to those of an actual aircraft (high Reynolds-number state) and enables significant improvement in the lift-drag ratio.
2. Description of the Related Art
In addition to normal lift-dependent drag and friction drag, a supersonic aircraft differs from a subsonic aircraft in that wave drag, arising from the occurrence of shock waves based on the compressibility of air, is further added (see FIG. 8), so that the lift-drag ratio (=lift/drag), which is an index of economic efficiency, is reduced. The Concorde, which has been the only commercial supersonic transport (SST) aircraft, has been plagued with problems of economic efficiency and environmental acceptability due to engine noise and sonic boom. Comparing the Boeing 747, which is representative of subsonic aircraft, and the Concorde, the lift-drag ratios of the two are approximately 14 and 7 respectively, and in development of a next-generation SST further improvement of this lift-drag ratio of 7 will be sought in order to improve economic efficiency (see K. Yoshida, “On fundamental research regarding aerodynamic shape of supersonic transports: an example of in-house research results”, Journal of The Japan Society For Aeronautical and Space Sciences, Vol. 42, No. 486 (1994), pp. I-13, and K. Yoshida, K. Suzuki, T. Iwamiya and F. Kuroda, “Reconsideration on Aerodynamic Design Concepts of the Scaled Supersonic Experimental Airplane—Comparison of the 1st Generation SST—”, 31st Annual Conference of the Japan Society for Aeronautical and Space Sciences, 2000).
In optimal aerodynamic design methods using computational fluid dynamics (Hereafter, it is abbreviated as CFD) which have been developed in recent years, attempts at design have been made which focus on reduction of pressure drag, of which the above-described wave drag is representative, and significant progress has been made compared with the era of Concorde development (see K. Yoshida, “Supersonic drag reduction technology in the scaled supersonic experimental airplane project by JAXA”, Progress in Aerospace Sciences, Vol. 45, No. 4-5, pp. 124-146 (2009)). A combination of CFD with a design method employing numerically optimized algorithms is thought to be in a stage capable of derivation of substantively optimal solutions within the range of various constraints on computing capacity and design (meaning constraints arising from such limitations as are imposed by structural design, equipment design, flight characteristics, and similar). Hence when further improvement is sought, rather than pressure drag, it is thought to be essential to attempt to reduce friction drag, which has not been examined for the design of actual supersonic aircraft to date. It is also here noted that this invention relates to reduction of friction drag.
In general, friction drag occurs based on the following physical mechanism. First, because air is viscous, the airflow velocity in very close proximity to the surface of an airframe is substantially the same as that on the surface, but in the normal direction from the surface the velocity increases sharply from zero to a velocity close to uniform flow, and consequently the velocity gradient in the normal direction in proximity to the airframe surface is extremely high. According to aerodynamics, the friction force exerted by air on an airframe surface is the product of this velocity gradient and the coefficient of viscosity of air. Hence the aim (principal object of design) of reducing the friction force acting on the airframe consists of reducing this coefficient of viscosity or the velocity gradient. The former is an aerodynamic physical constant, and so artificial control is difficult. Hence the principal object of design is to reduce the latter, the velocity gradient, in order to reduce friction drag.
Next, as general properties of the boundary layer, it is known that in the front portion of the airframe surface, comparatively stable laminar flow is maintained (this is called the laminar boundary layer), and that with rearward flow, this laminar flow collapses, changing to a spatially and temporally turbulent flow condition (this is called the turbulent boundary layer). This change is called the boundary layer transition. The phenomenon of boundary layer transition occurs through a process in which extremely slight disturbances included in the airflow are amplified within the laminar boundary layer extending to above a physical object, and induce nonstationary and spatially irregular fluctuations within the boundary layer (see FIG. 9). This property of amplification and attenuation of disturbances within the laminar boundary layer is called instability of the boundary layer; it is known that in general there exist two instability mechanisms (see FIG. 10). One is an instability wave arising from a transient distribution having an axis perpendicular to the direction of flow arising at a two-dimensional wing. This is normally called the Tollmien-Schlichting wave (T-S wave) in honor of the theoretical discoverers. So this instability is called the Tollmien-Schlichting instability (T-S instability).
The other is instability arising from velocity components within the boundary layer induced by a pressure gradient in the direction perpendicular to the direction of flow occurring on a three-dimensional swept wing. This is thought to correspond to a transient distribution having an axis in the flow direction. This flow is normally called “crossflow”, and so this instability is called the crossflow instability (C-F instability).
It is known that in the turbulent boundary layer which occurs through this boundary layer transition, due to the influence of unsteady and spatially irregular turbulence, the velocity at places only slightly removed from the wall face at which velocity is zero is greatly amplified, and the velocity gradient is much larger than in the laminar boundary layer, so that consequently the friction coefficient is approximately 7 times greater than for the laminar boundary layer, inducing a sharp increase in friction drag. Hence conceivable techniques for reducing friction drag are to introduce innovations into the shape of the object (the wing shape) so as to delay this boundary layer transition to as far downstream (rearward) as possible, or so as to artificially control the flow. In the former technique, a design innovation in the wing shape is employed; because the aim is a natural laminar flow achieved through the pressure distribution theresurrounding, this technique is called natural laminarization; in the latter technique active control of the boundary layer, such as through suction and venting, is performed, and so this technique is called laminar flow control.
This invention, described below, has as a principal object effective natural laminarization, which among this is most effective and is beneficial with respect to energy efficiency, and relates to a new design method which, in conventional supersonic aircraft designed with the goal of reducing pressure drag, enables natural laminarization of the main wing in order to enable further reduction of friction drag. In 1998 there had been no such attempts anywhere in the world, and the Japan Aerospace Exploration Agency (hereafter JAXA) was the first to make such an attempt in its project for the National EXperimental Supersonic Transport project (the NEXST project). In this project, an unmanned and scaled supersonic experimental airplane was designed and developed by assuming a case of a subsonic leading edge with the swept wing contained within the Mach cone; first a theoretical pressure distribution on the main wing upper surface causing the boundary layer transition occurring in proximity to the wing leading edge to be delayed significantly in the direction of the wing trailing edge was created, and then a new main wing design method to realize this distribution was developed (see K. Yoshida, “Supersonic drag reduction technology in the scaled supersonic experimental airplane project by JAXA”, Progress in Aerospace Sciences, Vol. 45, No. 4-5, pp. 124-146 (2009); K. Yoshida, “Overview of NAL's Program Including the Aerodynamic Design of the Scaled Supersonic Experimental Airplane”, Fluid Dynamics Research on Supersonic Aircraft of VKI, RTO Educational Notes 4, 1998; K. Yoshida and Y. Makino, “Aerodynamic Design of Unmanned and Scaled Supersonic Experimental Airplane in Japan”, ECCOMAS 2004; and K. Yoshida, “Flight Test Results of Supersonic Experimental Airplane (NEXST-1)”, Nagare, Journal of Japan Society of Fluid Mechanics, Vol. 25, pp. 321-328 (2006)).
FIG. 11 is a flow diagram showing the natural laminar flow wing design method developed in the NEXST project.
This wing design method is the reverse of the normal method of determining the pressure distribution given a shape, and comprises a technique, given a pressure distribution, of determining the shape. In this main wing design method, first a conventional entire airframe shape as an initial shape is prepared, designed with the goal of reducing the pressure drag; the target pressure coefficient distribution (Cp, target-upper) on the main wing upper surface is created based on a usual CFD analysis method and transition point prediction method (eN method; FIG. 9), while on the other hand, the main wing lower surface target Cp distribution (Cp, target-lower), is created by combining a difference between lower and upper surface pressure difference distribution (ΔCp, target) derived from a Carlson type warp wing design method with the design concept of reducing the lift-dependent drag, which is one type of pressure drag, with the main wing upper surface target Cp distribution (Cp, target-upper). Next, a CFD analysis method is applied to the main wing cross-sectional shape of the initial airframe shape, a new pressure distribution in the vicinity of this main wing cross-sectional shape is determined, and then the difference between this pressure distribution and the above target Cp distribution (Cp, target) is calculated; by repeating corrections to the main wing shape and CFD analysis until this calculated difference becomes smaller than a prescribed difference value (threshold), the main wing cross-sectional shape is determined (hereafter this method of shape determination is called the CFD-based inverse problem design method). Here, CFD is a flow field analysis technique based on numerical fluid dynamics, and the usual CFD analysis method, given a shape, uses CFD to determine a physical quantity of a flow field in the vicinity; the CFD-based inverse problem design method, given a pressure distribution which characterizes a flow field, determines a shape realizing this distribution by combining usual CFD analysis and the shape correction method. Hence when designing a main wing cross-sectional shape based on this main wing design method, it is essential that, among the main wing upper and lower surface target Cp distributions (Cp, target), the main wing upper surface target Cp distribution (Cp, target-upper) in particular be set (created) with high precision. As explained above, in the flight conditions (high-Reynolds number state) of a large-scale commercial supersonic transport (large-scale SST), there is no prior example of a large-scale SST having a natural laminar flow wing which reduces the friction drag on the wing upper surface, and so at present there is no public data whatsoever for the pressure distribution on the main wing upper surface which is effective for natural laminarization of the wing upper surface in the high-Reynolds number state. Further, creation of the target Cp distribution (Cp, target-upper) of this main wing upper surface requires an excessive amount of effort, since the pressure distribution must be set over the entire main wing surface along the wing chordwise direction from the wing leading edge to the wing trailing edge at each spanwise station.
The above-mentioned Cp distribution (i.e. pressure coefficient distribution) makes the pressure distribution more accurate, and the concept of Cp distribution is expressed same as the one of pressure distribution. Hereinafter, the above is adapted.
At JAXA, on the assumptions that in the NEXST project the standpoint of pressure drag reduction from the supersonic leading edge is superior, and that application is to a case of a subsonic leading edge with superior low-speed performance, first each of the above-described types of pressure drag reduction design concepts was applied in design using linear theoretical techniques (pressure drag reduction concepts 1, 2, 3 in FIG. 12A). Next, an attempt was made to develop a natural laminar flow wing design method limited to the main wing upper surface, using a CFD-based inverse problem design method. In this natural laminar flow wing design method, first a theoretical pressure distribution shape to delay the boundary layer transition on the main wing upper surface is found (FIG. 12B), then this theoretical pressure distribution is set as the target pressure distribution, using the above-described pressure drag reduction concept the designed shape is selected as the initial airframe initial shape, based on this wing cross-sectional shape the CFD analysis method is used to estimate the main wing upper and lower surface pressure distributions, and the CFD analysis is repeated, while making slight corrections to the main wing shape, until the difference between the estimated pressure distribution and the target pressure distribution becomes smaller than a fixed value. By means of a natural laminar flow wing design method based on a CFD-based inverse problem design method employing repetition of this usual CFD analysis and shape correction, a specific wing cross-sectional shape was designed (FIG. 12C). As the method of slight shape corrections used here, based on formulation of supersonic linear theory (lifting surface theory), and utilizing the fact that pressure changes and the camber and thickness changes are in a one-to-one relationship, numerical solution of an integral equation defining this relationship was employed.
The effect of a natural laminar flow wing designed in this way was first qualitatively validated in wind tunnel tests (FIG. 12D). Here, “qualitatively” means that, in the case of wind tunnel tests, because disturbances necessarily occur in the mechanism of the wind tunnel generating a supersonic airflow, the airflow from upstream already includes significant small turbulence, and this is combined with instability of the boundary layer so that there exists a physical mechanism promoting transition, and insofar as it is generally difficult to eliminate this influence (in rare and specific wind tunnel conditions, it has been possible to greatly suppress this wind tunnel airflow turbulence, but complete elimination has not been possible), it is thought that the effect of some airflow turbulence is exerted on the transition phenomenon. Hence at JAXA, an unmanned and scaled supersonic experimental airplane was manufactured, and validation of natural laminar flow wing design was conducted through an actual flight environment without airflow turbulence. The total length of the airframe of the experimental airplane was 11.5 m, and was an aircraft scaled down to 11% from the assumed size of an actual large-scale SST. As the result of analysis of transition data measured in the flight test, it was confirmed that at the design point the transition point was delayed approximately 40% along the wing chord length, and the effect of the natural laminar flow wing design concept in NEXST-1 experimental airplane was validated (see FIG. 12D and K. Yoshida, “Supersonic drag reduction technology in the scaled supersonic experimental airplane project by JAXA”, Progress in Aerospace Sciences, Vol. 45, No. 4-5, pp. 124-146 (2009)).
However, in these experiments, insofar as a scaled airplane of total length 11.5 m was used, the Reynolds number is also 11% of that of the assumed large-scale SST, and the above-described natural laminar flow wing design method developed in the NEXST project has problems from the standpoint of establishing techniques for application to actual aircraft design; it became clear that there is a need for considerable improvement of the target pressure distribution shape found in the design of NEXST-1 airplane (see Y. Ueda and K. Yoshida, “Numerical Study on Optimum Pressure Distribution for Supersonic Natural Laminar Flow Wing Design”, Proc. 32nd Fluid Dynamics Conference, 2000).
This is equivalent to an increase in Reynolds number causing strong amplification of instabilities in the boundary layer, so that creation of the target pressure distribution at the main wing upper surface should fully take into account the Reynolds number dependence. In particular, for high Reynolds numbers corresponding to actual aircraft, C-F instabilities are extremely strong, and in the target pressure distribution for the main wing upper surface found in the NEXST-1 actual airplane design as well, it was subsequently found that an adequate effect was not exhibited. Hence at JAXA, improvement of the pressure distribution so as to obtain a similar natural laminarization effect even for high Reynolds numbers equivalent to that of actual aircraft such as large-scale SSTs was studied. As a result, it was found, as one outcome, that if the accelerating gradient in proximity to the leading edge is made three times or more larger than during design of the NEXST-1 experimental airplane, an effect is obtained (see Y. Ueda and K. Yoshida, “Numerical Study on Optimum Pressure Distribution for Supersonic Natural Laminar Flow Wing Design”, Proc. 32nd Fluid Dynamics Conference, 2000), but in subsequent detailed analyses, it became clear that although the basic approach of this outcome was qualitatively reasonable, quantitatively the effect was not necessarily as estimated, and extensive refinement was necessary. The main reason for this was errors arising from the precision of the model in the transition analysis method used at that time. Moreover, a versatile natural laminar flow wing design method which could be applied to objects other than the main wing surface of a NEXST-1 experimental airplane had not been constructed. This invention resolves these problems.
Finally, as research on natural laminarization at supersonic speeds, there has been research conducted independently in the U.S. in substantially the same period as the above-described NEXST project (see I. Kroo, P. Sturdza, R. Tracy and J. Chase, “Natural Laminar Flow for Quiet and Efficient Supersonic Aircraft”, AIAA-2002-0146, 2002). This is a laminar flow wing design concept completely different from the natural laminar flow wing design concept of NEXST-1; whereas, as explained below, in the NEXST-1 design a technique of suppressing C-F instability is adopted, the essence of the design concept in the above research conducted in the U.S. has as a principal object the suppressing of T-S instability, and in contrast with a conventional main wing having a large sweep angle of 45° or greater, determined from the standpoint of reducing the pressure drag, a wing with a small sweep angle of approximately 10 to 20°, with a supersonic leading edge planform with a sharp leading edge, is addressed. When this leading edge has a characteristic cross-sectional shape with a sharp thin distribution, the pressure gradient in the flow direction reliably decreases monotonically, and so there is the advantage of an accelerating gradient which is effective for suppressing T-S instability; but because with the low aspect ratio the sweep angle is small, in the above-described range of approximately 10 to 20°, the lift-dependent drag increases, and it is thought that achievement of reductions in both friction drag and pressure drag is difficult. The effect of transition point delay through this technique has been visually confirmed in flight experiments with this main wing shape perpendicularly mounted to the lower fuselage of an F-15 fighter (however, the wing itself was equivalent to a scale model); an advanced engineering level with respect to confirmation of natural laminarization through an actual flight airframe is evident, but considering that a scale model was used (the Reynolds number did not correspond to that of an actual aircraft) and that simultaneous reduction of pressure drag was not attempted, this research is regarded as quite incomplete with respect to application to actual aircraft design. Moreover there is no research and activity development at all on natural laminarization in Europe, so that the utility of this invention can be emphasized.